Matrix Algebra: System of Equations

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the fifth topic where we talk about setting up simultaneous linear equations in matrix form, consistent and inconsistent system of equations, the rank of a matrix, conditions when unique, infinite number or no solutions exist, and finding the inverse of a square matrix.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. System of Equations
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How do I solve simultaneous linear equations given in equation form?

Many students ask me how do I do this or that in MATLAB.  So I thought why not have a small series of my next few blogs do that.  In this blog, I show you how to solve simultaneous linear equations given in equation form.

  • The MATLAB program link is here.
  • The HTML version of the MATLAB program is here.
  • DO NOT COPY AND PASTE THE PROGRAM BELOW BECAUSE THE SINGLE QUOTES DO NOT TRANSLATE TO THE CORRECT SINGLE QUOTES IN MATLAB EDITOR.  DOWNLOAD THE MATLAB PROGRAM INSTEAD

%% HOW DO I DO THAT IN MATLAB SERIES?
% In this series, I am answering questions that students have asked
% me about MATLAB.  Most of the questions relate to a mathematical
% procedure.

%% TOPIC
% How do I solve a set of simultaneous linear equations
% given in equation form?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/sle_equations.m;
% Last Revised : August 22, 2009;
% Abstract: This program shows you how to solve a set of
%     simultaneous linear equations given in equation form?
%           .
clc
clear all
clf

%% INTRODUCTION

disp(‘ABSTRACT’)
disp(‘   This program shows you how to solve a’)
disp(‘   set of simultaneous linear equations given in equation form’)
disp(‘ ‘)
disp(‘AUTHOR’)
disp(‘   Autar K Kaw of https://autarkaw.wordpress.com’)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://numericalmethods.eng.usf.edu/blog/sle_equations.m’)
disp(‘ ‘)
disp(‘LAST REVISED’)
disp(‘   August 22, 2009’)
disp(‘ ‘)

%% INPUTS
% Enter the equations
eqn1=’12*a+23*b+39*c=29′;
eqn2=’13*a+17*b+19*c=37′;
eqn3=’21*a+23*b+29*c=59’;
%% DISPLAYING INPUTS
disp(‘  ‘)
disp(‘INPUTS’)
disp(‘________________________’)
disp(‘Equations’)
disp(‘________________________’)
disp(eqn1)
disp(eqn2)
disp(eqn3)

%% THE CODE
% The solution
X=solve(eqn1,eqn2,eqn3);
% Assigning the output
a=double(X.a);
b=double(X.b);
c=double(X.c);
%% DISPLAYING OUTPUTS
disp(‘  ‘)
disp(‘OUTPUTS’)
disp(‘________________________’)
disp(‘Solution Vector’)
disp(‘________________________’)
fprintf(‘\nValue of a= %g’,a)
fprintf(‘\nValue of b= %g’,b)
fprintf(‘\nValue of c= %g’,c)
disp(‘  ‘)
disp(‘________________________’)

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos and http://www.youtube.com/numericalmethodsguy

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

How do I solve a set of simultaneous linear equations given in matrix form?

Many students ask me how do I do this or that in MATLAB.  So I thought why not have a small series of my next few blogs do that.  In this blog, I show you how to solve simultaneous linear equations given in matrix form.

  • The MATLAB program link is here.
  • The HTML version of the MATLAB program is here.
  • DO NOT COPY AND PASTE THE PROGRAM BELOW BECAUSE THE SINGLE QUOTES DO NOT TRANSLATE TO THE CORRECT SINGLE QUOTES IN MATLAB EDITOR.  DOWNLOAD THE MATLAB PROGRAM INSTEAD

%% HOW DO I DO THAT IN MATLAB SERIES?
% In this series, I am answering questions that students have asked
% me about MATLAB.  Most of the questions relate to a mathematical
% procedure.

%% TOPIC
% How do I solve a set of simultaneous linear equations?

%% SUMMARY

% Language : Matlab 2008a;
% Authors : Autar Kaw;
% Mfile available at
% http://numericalmethods.eng.usf.edu/blog/sle.m;
% Last Revised : August 12, 2009;
% Abstract: This program shows you how to solve a set of simultaneous linear
% equations?
%           .
clc
clear all
clf

%% INTRODUCTION

disp(‘ABSTRACT’)
disp(‘   This program shows you how to solve a’)
disp(‘   set of simultaneous linear equations’)
disp(‘ ‘)
disp(‘AUTHOR’)
disp(‘   Autar K Kaw of https://autarkaw.wordpress.com’)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://numericalmethods.eng.usf.edu/blog/sle.m’)
disp(‘ ‘)
disp(‘LAST REVISED’)
disp(‘   August 12, 2009’)
disp(‘ ‘)

%% INPUTS
% Enter the coefficient matrix of the equation [A][X]=[C]
A=[12  23  39; 13  17  19; 21  23  29];
% Enter the right hand side vector
C=[29;   37;  59];
%% DISPLAYING INPUTS
disp(‘  ‘)
disp(‘INPUTS’)
disp(‘________________________’)
disp(‘Coefficient Matrix’)
disp(‘________________________’)
dataval=[A];
disp(dataval)
disp(‘________________________’)
disp(‘Right hand side vector’)
disp(‘________________________’)
dataval=[C];
disp(dataval)
disp(‘________________________’)

%% THE CODE
% The solution
X=A\C;

%% DISPLAYING OUTPUTS
disp(‘  ‘)
disp(‘OUTPUTS’)
disp(‘________________________’)
disp(‘Solution Vector’)
disp(‘________________________’)
dataval=[X];
disp(dataval)
disp(‘________________________’)

his post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos and http://www.youtube.com/numericalmethodsguy

Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.